Due to the increasing use of the different composite materials in lightweight applications, such as in aerospace, it becomes crucial to understand the different damages occurring within them during life cycle and their possible inspection with different inspection techniques in different life cycle stages. A comprehensive classification of these damage patterns, measuring signals, and analysis methods using a taxonomical approach can help in this direction. In conjunction with the taxonomy, this work addresses damage diagnostics in hybrid and composite materials, such as fibre metal laminates (FMLs). A novel unified taxonomy atlas of damage patterns, measuring signals, and analysis methods is introduced. Analysis methods based on advanced supervised and unsupervised machine learning algorithms, such as autoencoders, self-organising maps, and convolutional neural networks, and a novel z-profiling method, are implemented. Besides formal aspects, an extended use case demonstrating damage identification in FML plates using X-ray computer tomography (X-ray CT) data is used to elaborate different data analysis techniques to amplify or detect damages and to show challenges.